How to polish curving edges?
The Grab brush (Shortcut "G") is great for getting the right shape for your curve.

What I'd use here would be the Fill/Deepen brush (shortcut "5") and the Flatten brush (shortcut "6"). Then I'd gently smooth the flat surfaces until close to the hard edge (shortcut "Shift"). 

If there's any edge that I was completely happy with, the pinch brush (Shortcut "P") is great for getting a sharper edge to finish it off.

Just play around with strength and keep undoing things if you make mistakes.

Sculpting these harder surfaces takes a bit of practise but it's generally the fastest way.

OR

If you don't feel comfortable with this, perhaps you could try retopologising it using a shrink wrap modifier and a vertex group. This way you can remove certain vertices from the shrinkwrap vertex group and play with a specific vertex until you're happy. With your retopologised mesh, you can play with the Mean Crease in properties panel ("N") underneath the transform data to get those edges nice a crisp when applying a subdivision surface.